A projection operator onto a closed convex set in Hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms. Moreover, it minimizes distance and is nonexpansive, and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds. In this paper, we exploit the properties of these operators t...
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The image restoration theory discussed in a previous paper by Youla and Webb [1] is applied to a simulated image and the results compared with the well-known method known as the Gerchberg-Papoulis algorithm. The results show that the method of image restoration by projection onto convex sets, by providing a convenient technique for utilizing a priori information, performs significantly better than...
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This paper is a first attempt at answering the question of which strong reflectors are most useful in ultrasound test objects. A planar reflector placed in the transducer far field has demonstrated potential as a standard reference reflector for pulse-echo ultrasound studies. Measurements of echo temporal voltage waveform and frequency spectrum from various metallic and plastic cylindrical reflect...
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Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density ?? = ??(x, y, z) generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate ??...
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This paper complements other studies in the field of image restoration in X-ray computed tomography by including the source collimator among the sources of image degradation. The overall blur is describable in terms of a space variant 2-D impulse response or point spread function, which is initially calculated for an arbitrary scanning eccentricity, a uniform source intensity distribution, a unifo...
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This paper clarifies that a method of rotary positron-emission computed tomography (PCT) with quad (tri or bi)-detector units can provide the satisfactory sampling characteristics with negligible sacrifice (less than 1 percent) of the detector packing ratio. This paper also presents the array design of quad-BGO (bismuth germanate) units and the sampling characteristics of a rotary PCT system named...
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A simple modification of the filtered backprojection algorithm is presented for the computation of the local statistical noise in emission computed tomography. The technique is general in that any distribution of radioactivity may be accommodated. When applied to positron emission tomography, it is shown that the effects of photon absorption, random coincidences, radioactive decay, and detector no...
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A low dose technique has been recently proposed for tomographic studies of the lung, which makes use of a gamma camera to detect 90?? Compton-scattered photons from external planar gamma source. In this paper, we present a detailed Monte Carlo study of this technique. A 20 ?? 20 ?? 20 cm3 water phantom was simulated as a target and a large gamma camera equipped with an imaging collimator as a dete...
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A dye-edge tracking algorithm was used to determine the corresponding points in the two images (anterior-posterior and lateral) of the digital subtraction biplane angiography. This correspondence was used to reconstruct three-dimensional images of cerebral arteries in a dog experiment and a clinical observation. The method was tested by comparing the measured image of oblique view to the computed ...
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The focus of the journal is on unifying the sciences of medicine, biology, and imaging. It emphasizes the common ground where instrumentation, hardware, software, mathematics, physics, biology, and medicine interact through new analysis methods. Strong application papers that describe novel methods are particularly encouraged. Papers describing important applications based on medically adopted and/or established methods without significant innovation in methodology will be directed to other journals.

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